Demographics

Everyone

Demographics for all included participants.

Demographics
Summary
N Age (years) Education (years) Sex (M/F/O) EHI
844 29.08 (6.03) 14.38 (2.48) 441/391/12 5.09 (79.37)



Race n
White 606
Black or African American 82
Multiple 76
Asian 69
American Indian or Alaska Native 5
Native Hawaiian or Other Pacific Islander 3
Other 3


Hispanic ethnicity n
No 744
Yes 100


By handedness group

Demographics for included participants, by handedness group (EHI bins).

Handedness N Age (years) Education (years) Sex (M/F/O) EHI
Left 331 28.84 (6.1) 14.45 (2.39) 170/157/4 -81.61 (19.27)
Mixed 135 28.83 (6.17) 14.58 (2.6) 77/56/2 -8.89 (26.49)
Right 378 29.38 (5.93) 14.24 (2.5) 194/178/6 86.01 (16.61)
Left: (EHI <= -40) | Mixed: (-40 < EHI < 40) | Right: (EHI >= 40)


Field x Level x Handedness (binned)

Do we find an interaction of field x level x handedness, when handedness is binned as left (EHI <= -40) or right (EHI > +40)?

Summary. For reaction time, we find the critical interaction in the predicted direction (11.67ms, 95% CI [0.65, 22.69], p = .019, one-sided). Left handers show 15.64ms LVF global bias (95% CI [7.61, 23.67]), and right handers 27.31ms (95% CI [19.80, 34.81]). Mixed handers (not included in the categorical interaction analysis) show a LVF global bias of 21.66ms (95% CI [9.09, 34.23]).

For accuracy, we find no significant interaction of field by level by handedness (OR = 0.90, 95% CI [0.70, 1.16], p = .42; where OR < 1 means greater LVF global bias for left handers). Point estimates of LVF global bias hardly differ between left handers (OR = 1.95, 95% CI [1.62, 2.35]) and right handers (OR = 1.77, 95% CI [1.49, 2.10]). For mixed handers (not included in the categorical interaction analysis), the point estimate is 1.10 (95% CI [0.82, 1.47])



Reaction time

Plots

Error bars show 95% CI.



Statistics

Simple mixed regression model

Reaction time is modeled as a linear effect of field, level, and handedness, using data from every target-present trial with a “go” response:

lmer( rt ~ field*level*handedness + (1 | subject) )


Field by level by handedness interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
9 1,166,282.858 1,166,367.139 −583,132.429 1,166,264.858 - - -
10 1,166,280.551 1,166,374.197 −583,130.276 1,166,260.551 4.307 1 .038
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by handedness interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Right - Left 11.666 5.622 Inf 0.648 22.685 2.075 .038
1 A positive number means LVF global bias is stronger in right handers (as predicted by AAH)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


LVF Global bias by handedness bin (RT)
field_consec level_consec handedness estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF - RVF Local - Global Left 15.641 4.096 Inf 7.613 23.669 3.819 .0001
LVF - RVF Local - Global Mixed 21.658 6.414 Inf 9.087 34.228 3.377 .0007
LVF - RVF Local - Global Right 27.307 3.829 Inf 19.802 34.812 7.131 <.0001
1 A positive number means global bias (faster RT for global)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided, uncorrected


Field by level interaction (RT)
Old-school Omnibus F-test
term df sumsq meansq statistic p.value
field 1 1,664,691.722 1,664,691.722 23.612 <.0001
level 1 9,626,122.373 9,626,122.373 136.54 <.0001
handedness 1 10,185,712.46 10,185,712.46 144.477 <.0001
field:level 1 2,730,949.837 2,730,949.837 38.737 <.0001
field:handedness 1 1,505,316.949 1,505,316.949 21.352 <.0001
level:handedness 1 12,247.994 12,247.994 0.174 .677
field:level:handedness 1 127,954.685 127,954.685 1.815 .178
Residuals 86,205 6,077,502,195.866 70,500.576 - -
 



summary(rt_model_2bins)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field * level * handedness + (1 | subject)
##    Data: aah_for_rt_model_2bins
## 
## REML criterion at convergence: 1166226.1
## 
## Scaled residuals: 
##       Min        1Q    Median        3Q       Max 
## -4.871042 -0.589962 -0.165354  0.361143  7.634801 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  subject  (Intercept) 28355.6  168.391 
##  Residual             42345.3  205.780 
## Number of obs: 86213, groups:  subject, 709
## 
## Fixed effects:
##                                      Estimate Std. Error  t value
## (Intercept)                         663.50167    9.47901 69.99697
## fieldLVF                            -25.29475    2.87911 -8.78560
## levelLocal                           13.71496    2.91027  4.71261
## handednessRight                      18.61377   12.98209  1.43380
## fieldLVF:levelLocal                  15.64117    4.10675  3.80865
## fieldLVF:handednessRight             10.27036    3.94550  2.60306
## levelLocal:handednessRight           -6.47365    3.98194 -1.62575
## fieldLVF:levelLocal:handednessRight  11.66629    5.62176  2.07520
## 
## Correlation of Fixed Effects:
##             (Intr) fldLVF lvlLcl hnddnR flLVF:L fLVF:R lvlL:R
## fieldLVF    -0.153                                           
## levelLocal  -0.152  0.499                                    
## hnddnssRght -0.730  0.112  0.111                             
## fldLVF:lvlL  0.107 -0.701 -0.707 -0.078                      
## fldLVF:hndR  0.112 -0.730 -0.364 -0.153  0.512               
## lvlLcl:hndR  0.111 -0.365 -0.731 -0.152  0.517   0.500       
## fldLVF:lL:R -0.079  0.512  0.517  0.108 -0.731  -0.702 -0.707


Accuracy

Plots

Error bars show 95% CI.


Statistics

Simple mixed regression model

Accuracy is modeled as a binomial effect of field, level, and handedness, using binary correct/incorrect data from every target-present trial:

glmer( correct ~ field*level*handedness + (1 | subject), family = "binomial" )


Field by level by handedness interaction (Accuracy)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
8 32,836.316 32,911.643 −16,410.158 32,820.316 - - -
9 32,837.667 32,922.41 −16,409.833 32,819.667 0.649 1 .42
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by handedness interaction (Accuracy)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness_consec odds.ratio1 SE df2 asymp.LCL3 asymp.UCL3 null z.ratio p.value4
LVF / RVF Global / Local Right / Left 0.899 0.118 Inf 0.696 1.162 1 −0.814 .416
1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF for right handers (predicted by AAH)
2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp.
3 Confidence level: 95%
4 Two-sided


LVF Global bias by handedness bin (Accuracy)
Compare effect estimate to zero with emmeans()
field_consec level_consec handedness odds.ratio1 SE df2 asymp.LCL3 asymp.UCL3 null z.ratio p.value4
LVF / RVF Global / Local Left 1.954 0.185 Inf 1.623 2.353 1 7.063 <.0001
LVF / RVF Global / Local Mixed 1.097 0.162 Inf 0.821 1.465 1 0.626 .532
LVF / RVF Global / Local Right 1.766 0.154 Inf 1.488 2.095 1 6.514 <.0001
1 Backtransformed to odds ratio from log odds ratio (tests are performed on log odds ratio scale). A ratio > 1 means global bias is stronger in the LVF, as predicted for right handers. Mixed handers' global bias is shown here, but their data was not included in the binomial model.
2 'Inf' df is expected when emmeans does logistic regression. See emmeans FAQ: https://cran.r-project.org/web/packages/emmeans/vignettes/FAQs.html#asymp.
3 Confidence level: 95%
4 Two-sided 



summary(acc_model_2bins)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
##    Data: aah_for_acc_model_2bins
## 
##      AIC      BIC   logLik deviance df.resid 
##  32837.7  32922.4 -16409.8  32819.7    90743 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -12.046183   0.123597   0.170659   0.240743   1.070559 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.03569  1.01769 
## Number of obs: 90752, groups:  subject, 709
## 
## Fixed effects:
##                                        Estimate Std. Error  z value
## (Intercept)                           3.1227080  0.0719596 43.39530
## fieldLVF                             -0.1101649  0.0563127 -1.95631
## levelGlobal                           0.4277909  0.0630223  6.78793
## handednessRight                       0.1047397  0.0983966  1.06446
## fieldLVF:levelGlobal                  0.6731050  0.0962270  6.99497
## fieldLVF:handednessRight             -0.0341608  0.0784866 -0.43524
## levelGlobal:handednessRight          -0.1561983  0.0867458 -1.80064
## fieldLVF:levelGlobal:handednessRight -0.1065265  0.1308698 -0.81399
##                                                Pr(>|z|)    
## (Intercept)                                  < 2.22e-16 ***
## fieldLVF                                       0.050429 .  
## levelGlobal                          0.0000000000113752 ***
## handednessRight                                0.287118    
## fieldLVF:levelGlobal                 0.0000000000026532 ***
## fieldLVF:handednessRight                       0.663386    
## levelGlobal:handednessRight                    0.071759 .  
## fieldLVF:levelGlobal:handednessRight           0.415651    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF    -0.410                                           
## levelGlobal -0.361  0.467                                    
## hnddnssRght -0.718  0.301  0.266                             
## fldLVF:lvlG  0.244 -0.589 -0.656 -0.180                      
## fldLVF:hndR  0.295 -0.720 -0.338 -0.421  0.426               
## lvlGlbl:hnR  0.264 -0.342 -0.730 -0.377  0.481   0.478       
## fldLVF:lG:R -0.181  0.436  0.487  0.257 -0.740  -0.605 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00965947 (tol = 0.002, component 1)


Using the bobyqa optimizer alone gives virtually the same results.

summary(acc_model_2bins_bobyqa)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
##    Data: aah_for_acc_model_2bins
## Control: glmerControl(optimizer = c("bobyqa"))
## 
##      AIC      BIC   logLik deviance df.resid 
##  32837.7  32922.4 -16409.8  32819.7    90743 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -12.045085   0.123596   0.170659   0.240752   1.070436 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.03554  1.01762 
## Number of obs: 90752, groups:  subject, 709
## 
## Fixed effects:
##                                        Estimate Std. Error  z value
## (Intercept)                           3.1227181  0.0717392 43.52878
## fieldLVF                             -0.1101583  0.0561263 -1.96269
## levelGlobal                           0.4271459  0.0626393  6.81913
## handednessRight                       0.1047658  0.0980956  1.06800
## fieldLVF:levelGlobal                  0.6734926  0.0955733  7.04687
## fieldLVF:handednessRight             -0.0341812  0.0782540 -0.43680
## levelGlobal:handednessRight          -0.1555689  0.0862525 -1.80364
## fieldLVF:levelGlobal:handednessRight -0.1068799  0.1300024 -0.82214
##                                                Pr(>|z|)    
## (Intercept)                                  < 2.22e-16 ***
## fieldLVF                                       0.049683 *  
## levelGlobal                          0.0000000000091593 ***
## handednessRight                                0.285522    
## fieldLVF:levelGlobal                 0.0000000000018299 ***
## fieldLVF:handednessRight                       0.662258    
## levelGlobal:handednessRight                    0.071287 .  
## fieldLVF:levelGlobal:handednessRight           0.410999    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF    -0.407                                           
## levelGlobal -0.357  0.463                                    
## hnddnssRght -0.716  0.298  0.263                             
## fldLVF:lvlG  0.241 -0.585 -0.653 -0.176                      
## fldLVF:hndR  0.292 -0.719 -0.334 -0.419  0.422               
## lvlGlbl:hnR  0.260 -0.338 -0.727 -0.375  0.476   0.475       
## fldLVF:lG:R -0.177  0.432  0.482  0.254 -0.737  -0.602 -0.664


Field x Level x Handedness (continuous)

Do we find an interaction of field x level x handedness (continuous EHI score)?

Summary. For reaction time, we find the critical interaction in the predicted direction (.067ms per EHI unit, 95% CI [0.003, 0.13], p = .020, one-sided). Estimated global bias is 13.32ms lower for strong left handers (EHI -100: 14.82ms, 95% CI [6.48, 23.17]) than for strong right handers (EHI +100: 28.14ms, 95% CI [20.31, 35.98]).

For accuracy, we find no significant interaction of field by level by EHI (Beta = 0.0002 logodds per EHI unit, 95% CI [-0.001, 0.002], p = .81). Estimated LVF global bias hardly differs for strong left handers (EHI -100: OR = 1.67, 95% CI [1.37, 2.03]) and strong right handers (EHI +100: OR = 1.73, 95% CI [1.45, 2.07]).



Reaction time

Plots

Statistics

Model RT as a linear effect of field, level, and EHI (continuous):

rt_model_ehi <- lmer( rt ~ field*level*ehi + (1 | subject) )

Field by level by ehi interaction (RT)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
9 1,387,640.958 1,387,726.807 −693,811.479 1,387,622.958 - - -
10 1,387,638.71 1,387,734.097 −693,809.355 1,387,618.71 4.248 1 .039
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level interaction (RT)
Compare effect estimate to zero with emmeans()
field_consec level_consec estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
RVF - LVF Global - Local 0.067 0.032 Inf 0.003 0.13 2.061 .039
1 A positive number means global bias is stronger in LVF for right handers (as predicted by AAH), in ms per EHI unit (-100 to 100). Multiply this value by 200 to get the estimated difference in LVF global bias for strong left vs. right handers.
2 Z-approximation
3 Confidence level: 95
4 Two-sided


Field by level interaction (RT)
Compare effect estimate to zero with emmeans()
contrast estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF Local - LVF Global 0.033 0.023 Inf −0.025 0.092 1.459 .463
RVF Local - RVF Global −0.033 0.023 Inf −0.092 0.026 −1.454 .465
1 A positive number means more global bias for right handers, in ms per EHI unit (-100 to 100)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided


Slope of EHI and RT by field and level
Compare effect estimate to zero with emmeans()
field level ehi.trend1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF Local 0.219 0.075 Inf 0.073 0.366 2.93 .003
RVF Local 0.096 0.075 Inf −0.05 0.243 1.288 .198
LVF Global 0.186 0.075 Inf 0.039 0.332 2.487 .013
RVF Global 0.13 0.075 Inf −0.017 0.276 1.734 .083
1 A positive number means slower RTs for right handers, in ms per EHI unit (-100 to 100).
2 Z-approximation
3 Confidence level: 95%
4 Two-sided



Estimated LVF global bias, by EHI score
field_consec level_consec ehi1 estimate2 SE df asymp.LCL asymp.UCL z.ratio p.value
RVF - LVF Global - Local −100 14.822 4.257 Inf 6.479 23.166 3.482 .0005
RVF - LVF Global - Local 0 21.483 2.569 Inf 16.447 26.519 8.361 <.0001
RVF - LVF Global - Local 100 28.144 3.996 Inf 20.311 35.976 7.042 <.0001
1 Strong left hander: -100; Mixed hander: 0; Strong right hander: +100
2 Estimated LVF global bias (ms); a positive number means LVF global bias


Estimated global bias by field, by EHI score
contrast ehi estimate1 SE df asymp.LCL asymp.UCL z.ratio p.value
LVF Local - LVF Global −100 29.412 3.009 Inf 21.683 37.141 9.776 <.0001
RVF Local - RVF Global −100 14.59 3.016 Inf 6.841 22.339 4.837 <.0001
LVF Local - LVF Global 0 32.743 1.816 Inf 28.077 37.409 18.028 <.0001
RVF Local - RVF Global 0 11.26 1.82 Inf 6.586 15.935 6.188 <.0001
LVF Local - LVF Global 100 36.074 2.824 Inf 28.82 43.328 12.775 <.0001
RVF Local - RVF Global 100 7.93 2.83 Inf 0.66 15.201 2.802 .026
1 Estimated global bias (ms); a positive number means global bias


Reaction time by field and level, by EHI score
field level ehi prediction1 asymp.LCL asymp.UCL
LVF Local −100 658.263 638.967 677.559
RVF Local −100 667.869 648.575 687.163
LVF Global −100 628.851 609.576 648.126
RVF Global −100 653.279 633.997 672.561
LVF Local 0 680.17 668.522 691.818
RVF Local 0 677.494 665.848 689.14
LVF Global 0 647.427 635.791 659.063
RVF Global 0 666.234 654.594 677.874
LVF Local 100 702.077 683.953 720.201
RVF Local 100 687.119 668.998 705.24
LVF Global 100 666.002 647.895 684.11
RVF Global 100 679.189 661.074 697.303
1 Reaction time (ms)


\[ 28.144 - 14.822 = 13.322ms \\ 13.322/200 = 0.067ms / EHI unit \] The model estimates that an average strong right hander (EHI +100) will have 13.32ms more LVF global bias than a strong left hander (EHI -100). Each unit change in EHI (-100:100) corresponds to a 0.067ms difference in LVF global bias. This is also the slope estimate given by the summary function: 

summary(rt_model_ehi)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field:level:ehi + field:level + field:ehi + level:ehi +  
##     field + level + ehi + (1 | subject)
##    Data: aah_for_rt_ehi_model
## 
## REML criterion at convergence: 1387626.2
## 
## Scaled residuals: 
##       Min        1Q    Median        3Q       Max 
## -4.879612 -0.590631 -0.167132  0.363313  7.653749 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  subject  (Intercept) 28269.4  168.135 
##  Residual             42128.7  205.253 
## Number of obs: 102615, groups:  subject, 844
## 
## Fixed effects:
##                             Estimate  Std. Error   t value
## (Intercept)              680.1697334   5.9429525 114.44980
## fieldRVF                  -2.6755865   1.8307862  -1.46144
## levelGlobal              -32.7431087   1.8162558 -18.02781
## ehi                        0.2190687   0.0747656   2.93007
## fieldRVF:levelGlobal      21.4828945   2.5694569   8.36087
## fieldRVF:ehi              -0.1228165   0.0230212  -5.33493
## levelGlobal:ehi           -0.0333102   0.0228331  -1.45886
## fieldRVF:levelGlobal:ehi   0.0666075   0.0323174   2.06104
## 
## Correlation of Fixed Effects:
##             (Intr) fldRVF lvlGlb ehi    flRVF:G flRVF: lvlGl:
## fieldRVF    -0.155                                           
## levelGlobal -0.156  0.506                                    
## ehi         -0.064  0.010  0.010                             
## fldRVF:lvlG  0.110 -0.713 -0.706 -0.007                      
## fieldRVF:eh  0.010 -0.067 -0.033 -0.154  0.047               
## levelGlbl:h  0.010 -0.033 -0.065 -0.156  0.046   0.506       
## fldRVF:lvG: -0.007  0.047  0.046  0.110 -0.065  -0.712 -0.706


Accuracy

Plots

Statistics

Model accuracy as a binomial effect of field, level, and EHI (continuous):

acc_ehi_model <- glmer( rt ~ field*level*ehi + (1 | subject), family = "binomial" )


Field by level by EHI interaction (Accuracy)
ANOVA: compare models with vs. without interaction term
npar AIC BIC logLik deviance Chisq Df p.value1
8 39,111.468 39,188.189 −19,547.734 39,095.468 - - -
9 39,113.409 39,199.72 −19,547.704 39,095.409 0.059 1 .808
1 F-test (two-sided? https://daniellakens.blogspot.com/2016/04/one-sided-f-tests-and-halving-p-values.html)


Field by level by EHI interaction (Accuracy)
Compare effect estimate to zero with emmeans()
field_consec level_consec estimate1 SE df asymp.LCL2 asymp.UCL2 z.ratio p.value3
RVF - LVF Local - Global 0.0002 0.0007 Inf −0.0013 0.0017 0.2491 .803
1 A positive number means global bias is stronger in LVF for right handers (as predicted), in logodds per EHI unit (-100 to 100). Multiply this value by 200 to get the estimated difference in LVF global bias for strong left vs. right handers.
2 Confidence level: 95% (two-sided)
3 Two-sided


Field by level interaction (Accuracy)
contrast estimate1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF Global - LVF Local −0.001 0.0006 Inf −0.0021 0.0001 −1.8003 .072
RVF Global - RVF Local −0.0012 0.0005 Inf −0.0022 −0.0002 −2.3594 .018
1 A positive number means more global bias, in logodds per EHI unit (-100 to 100)
2 Z-approximation
3 Confidence level: 95%
4 Two-sided, uncorrected


Slope of EHI and Accuracy by field and level
Compare effect estimate to zero with emmeans()
field level ehi.trend1 SE df2 asymp.LCL3 asymp.UCL3 z.ratio p.value4
LVF Global −0.0007 0.0007 Inf −0.002 0.0006 −1.0258 .305
RVF Global −0.0006 0.0006 Inf −0.0018 0.0006 −0.9557 .339
LVF Local 0.0003 0.0006 Inf −0.0008 0.0014 0.5793 .562
RVF Local 0.0006 0.0006 Inf −0.0005 0.0017 1.0666 .286
1 A positive number means higher accuracy for right handers, in logodds per EHI unit (-100 to 100).
2 Z-approximation
3 Confidence level: 95%
4 Two-sided



Estimated LVF global bias, by EHI score
field_consec level_consec ehi1 odds.ratio2 SE df asymp.LCL asymp.UCL null z.ratio p.value
RVF / LVF Local / Global -100 1.67 0.166 Inf 1.374 2.028 1 5.164 <.0001
RVF / LVF Local / Global 0 1.701 0.101 Inf 1.514 1.911 1 8.942 <.0001
RVF / LVF Local / Global 100 1.733 0.159 Inf 1.448 2.074 1 5.996 <.0001
1 Strong left hander: -100; Mixed hander: 0; Strong right hander: +100
2 Estimated LVF global bias. An odds ratio > 1 means LVF global bias.


Estimated global bias by field, by EHI score
contrast ehi odds.ratio1 SE df asymp.LCL asymp.UCL null z.ratio p.value
LVF Global / LVF Local -100 2.83 0.209 Inf 2.341 3.422 1 14.075 <.0001
RVF Global / RVF Local -100 1.695 0.112 Inf 1.429 2.01 1 7.953 <.0001
LVF Global / LVF Local 0 2.561 0.113 Inf 2.287 2.868 1 21.336 <.0001
RVF Global / RVF Local 0 1.506 0.06 Inf 1.359 1.668 1 10.266 <.0001
LVF Global / LVF Local 100 2.317 0.157 Inf 1.947 2.758 1 12.409 <.0001
RVF Global / RVF Local 100 1.337 0.083 Inf 1.141 1.567 1 4.697 <.0001
1 Estimated global bias. An odds ratio > 1 means global bias.


Accurracy by field and level, by EHI score
field level ehi prob1 asymp.LCL asymp.UCL
LVF Global −100 0.983 0.98 0.986
RVF Global −100 0.974 0.97 0.978
LVF Local −100 0.953 0.947 0.96
RVF Local −100 0.957 0.951 0.963
LVF Global 0 0.982 0.98 0.984
RVF Global 0 0.973 0.97 0.975
LVF Local 0 0.955 0.951 0.959
RVF Local 0 0.959 0.956 0.963
LVF Global 100 0.981 0.977 0.983
RVF Global 100 0.971 0.967 0.975
LVF Local 100 0.956 0.95 0.962
RVF Local 100 0.962 0.956 0.967
1 Accuracy (% correct)


\[ log(1.73) = .548 \] \[ log(1.67) = .513 \] \[ log(1.73) - log(1.67) = .0353 \] \[ .0353 / 200 = -0.000185 logodds / EHI unit \] The model estimates that a strong right hander (EHI +100) will have 1.73/1.67 = 1.04 greater odds of correctness for LVF global stimuli versus a strong left hander (EHI -100). Each unit change in EHI (-100:100) corresponds to a 0.0002 (logodds) difference in LVF global bias. This matches the slope estimate given by the summary function: 

summary(acc_model_ehi)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
##    Data: aah_for_acc_ehi_model
## 
##      AIC      BIC   logLik deviance df.resid 
##  39113.4  39199.7 -19547.7  39095.4   108023 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -11.748088   0.117364   0.168282   0.238851   1.067892 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.05841  1.02879 
## Number of obs: 108032, groups:  subject, 844
## 
## Fixed effects:
##                              Estimate    Std. Error   z value Pr(>|z|)    
## (Intercept)              3.9930184017  0.0532670291  74.96229  < 2e-16 ***
## fieldRVF                -0.4209327473  0.0474500751  -8.87107  < 2e-16 ***
## levelLocal              -0.9403339363  0.0440725615 -21.33604  < 2e-16 ***
## ehi                     -0.0006744722  0.0006575342  -1.02576 0.305005    
## fieldRVF:levelLocal      0.5311871060  0.0594032015   8.94206  < 2e-16 ***
## fieldRVF:ehi             0.0000955515  0.0005978575   0.15982 0.873020    
## levelLocal:ehi           0.0009994867  0.0005551631   1.80035 0.071806 .  
## fieldRVF:levelLocal:ehi  0.0001864551  0.0007484763   0.24911 0.803273    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldRVF lvlLcl ehi    flRVF:L flRVF: lvlLc:
## fieldRVF    -0.528                                           
## levelLocal  -0.575  0.636                                    
## ehi         -0.084  0.058  0.064                             
## fldRVF:lvlL  0.423 -0.799 -0.742 -0.046                      
## fieldRVF:eh  0.057 -0.105 -0.069 -0.538  0.084               
## levelLocl:h  0.063 -0.069 -0.090 -0.583  0.066   0.635       
## fldRVF:lvL: -0.045  0.084  0.066  0.430 -0.081  -0.799 -0.741
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00445801 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?


Using the bobyqa optimizer alone gives virtually the same results.

summary(acc_model_ehi_bobyqa)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
##    Data: aah_for_acc_ehi_model
## Control: glmerControl(optimizer = c("bobyqa"))
## 
##      AIC      BIC   logLik deviance df.resid 
##  39113.4  39199.7 -19547.7  39095.4   108023 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -11.747602   0.117369   0.168279   0.238853   1.067891 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.05839  1.02878 
## Number of obs: 108032, groups:  subject, 844
## 
## Fixed effects:
##                              Estimate    Std. Error   z value Pr(>|z|)    
## (Intercept)              3.9929178907  0.0532179046  75.02960  < 2e-16 ***
## fieldRVF                -0.4208114420  0.0473856786  -8.88056  < 2e-16 ***
## levelLocal              -0.9402494214  0.0439959119 -21.37129  < 2e-16 ***
## ehi                     -0.0006745785  0.0006575130  -1.02595 0.304913    
## fieldRVF:levelLocal      0.5310456792  0.0593024543   8.95487  < 2e-16 ***
## fieldRVF:ehi             0.0000955453  0.0005978400   0.15982 0.873025    
## levelLocal:ehi           0.0009996768  0.0005551421   1.80076 0.071741 .  
## fieldRVF:levelLocal:ehi  0.0001862092  0.0007484593   0.24879 0.803523    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldRVF lvlLcl ehi    flRVF:L flRVF: lvlLc:
## fieldRVF    -0.528                                           
## levelLocal  -0.575  0.635                                    
## ehi         -0.084  0.058  0.064                             
## fldRVF:lvlL  0.423 -0.799 -0.741 -0.046                      
## fieldRVF:eh  0.057 -0.105 -0.068 -0.538  0.084               
## levelLocl:h  0.063 -0.068 -0.089 -0.583  0.066   0.635       
## fldRVF:lvL: -0.045  0.084  0.066  0.430 -0.081  -0.799 -0.741
## optimizer (bobyqa) convergence code: 0 (OK)
## Model is nearly unidentifiable: very large eigenvalue
##  - Rescale variables?


Using a model with scaled EHI gives virtually the same results, and no warning about large eigenvalues.

summary(acc_model_ehi_scaled)
## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
##    Data: df_scaled
## Control: glmerControl(optimizer = c("bobyqa"))
## 
##      AIC      BIC   logLik deviance df.resid 
##  39113.4  39199.7 -19547.7  39095.4   108023 
## 
## Scaled residuals: 
##        Min         1Q     Median         3Q        Max 
## -11.748116   0.117364   0.168282   0.238852   1.067899 
## 
## Random effects:
##  Groups  Name        Variance Std.Dev.
##  subject (Intercept) 1.05841  1.02879 
## Number of obs: 108032, groups:  subject, 844
## 
## Fixed effects:
##                            Estimate  Std. Error   z value Pr(>|z|)    
## (Intercept)              3.98957057  0.05297442  75.31126  < 2e-16 ***
## fieldRVF                -0.42043214  0.04708796  -8.92866  < 2e-16 ***
## levelLocal              -0.93523445  0.04377379 -21.36517  < 2e-16 ***
## ehi                     -0.05351304  0.05210742  -1.02698  0.30443    
## fieldRVF:levelLocal      0.53211973  0.05901373   9.01688  < 2e-16 ***
## fieldRVF:ehi             0.00758447  0.04735701   0.16016  0.87276    
## levelLocal:ehi           0.07929785  0.04397042   1.80344  0.07132 .  
## fieldRVF:levelLocal:ehi  0.01477039  0.05927051   0.24920  0.80320    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) fldRVF lvlLcl ehi    flRVF:L flRVF: lvlLc:
## fieldRVF    -0.526                                           
## levelLocal  -0.572  0.633                                    
## ehi         -0.021  0.023  0.026                             
## fldRVF:lvlL  0.420 -0.797 -0.740 -0.018                      
## fieldRVF:eh  0.023 -0.041 -0.027 -0.537  0.032               
## levelLocl:h  0.026 -0.028 -0.025 -0.583  0.018   0.634       
## fldRVF:lvL: -0.018  0.033  0.018  0.429 -0.016  -0.798 -0.740